The Non-Slender Rank of an Abelian Group

Abstract

For a family (Ai)i∈I of Abelian groups and a cardinal K we define the K-product \(\mathop \Pi \limits_{i \in I} {A_i}\)
to be the subgroup of the cartesian product \({\mathop \Pi \limits_I ^{(K)}}A\)
consisting of all elements which support is less than K. Let us write AI(K) instead of \({A^{I(w)}} = \mathop \oplus \limits_I A\), A(I) instead of (math) and A[I] instead of AI(W1) . We are going to use the groups Z[K] to introduce a new cardinal invariant for an abelian group.